Question

A-1/a=2 so what is (a)2-1/(a2)

Answer 1

Answer:

4√2

Step-by-step explanation:

Given---> a - 1 / a = 2

To find ---> a² - 1 / a²

Solution---> ATQ,

a - 1 / a = 2

Squaring both sides,

=> ( a - 1 / a )² = 2²

=> a² + 1 / a² - 2 ( a ) ( 1 / a ) = 4

=> a² + 1 / a² - 2 = 4

=> a² + 1 / a² = 4 + 2

=> a² + 1 / a² = 6

Now, ( a + 1 / a )² = a² + 1 / a² + 2 ( a ) ( 1 / a )

= ( a² + 1 / a² ) + 2

= ( 6 ) + 2

( a + 1 / a )² = 8

=> ( a + 1 / a ) = √8

=> ( a + 1 / a ) = 2√2

Now, a² - 1 / a² = ( a )² - ( 1 / a )²

= ( a + 1 / a ) ( a - 1 / a )

= ( 2√2 ) ( 2 )

= 4√2

#Answerwithquality

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